Pathways to Math Literacy (Loose Leaf)
1st Edition
ISBN: 9781259218859
Author: David Sobecki Professor, Brian A. Mercer
Publisher: McGraw-Hill Education
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Chapter 4.5, Problem 2R
To determine
The reason why the inverse variation is a topic in the unit ‘Where’s my jetpack’.
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Problem1
We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
Chapter 4 Solutions
Pathways to Math Literacy (Loose Leaf)
Ch. 4.1 - After reading the opening paragraph, what do you...Ch. 4.1 - Prob. 1GCh. 4.1 - Prob. 2GCh. 4.1 - Prob. 3GCh. 4.1 - Prob. 4GCh. 4.1 - Prob. 5GCh. 4.1 - Prob. 6GCh. 4.1 - Prob. 1CCh. 4.1 - Prob. 2CCh. 4.1 - Prob. 3C
Ch. 4.1 - Prob. 4CCh. 4.1 - Prob. 5CCh. 4.1 - This phenomenon is so common, in fact, that data...Ch. 4.1 - Find the standard deviation for Ji-Mins golf...Ch. 4.1 - Discuss how comparing the two standard deviations...Ch. 4.1 - A standard package of Oreos is supposed to contain...Ch. 4.1 - A standard package of Oreos is supposed to contain...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - As our friend Mr. Twain pointed out over 100 years...Ch. 4.1 - As our friend Mr. Twain pointed out over 100 years...Ch. 4.1 - As our friend Mr. Twain pointed out over 100 years...Ch. 4.1 - Prob. 1RCh. 4.1 - Prob. 2RCh. 4.1 - Prob. 3RCh. 4.1 - Prob. 4RCh. 4.1 - Prob. 1ACh. 4.1 - Prob. 2ACh. 4.1 - Prob. 3ACh. 4.1 - In a group of 500 women, how many would you expect...Ch. 4.1 - Prob. 5ACh. 4.1 - Prob. 6ACh. 4.2 - Prob. 0LOCh. 4.2 - Prob. 1CCh. 4.2 - Prob. 2CCh. 4.2 - Prob. 3CCh. 4.2 - Prob. 4CCh. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - Prob. 5CACh. 4.2 - Suppose that we know that the distance between...Ch. 4.2 - How does the distance between points P and Q...Ch. 4.2 - The lower illustration also shows points P, Q, M,...Ch. 4.2 - Based on the scale provided on the two-dimensional...Ch. 4.2 - Illustrate the grade of each trail by drawing a...Ch. 4.2 - Use the Pythagorean theorem to estimate the true...Ch. 4.2 - Prob. 7GCh. 4.2 - How far would you actually drive in covering that...Ch. 4.2 - Prob. 9GCh. 4.2 - Prob. 11GCh. 4.2 - What does the Pythagorean theorem say? When can...Ch. 4.2 - Why cant you just find the distance between two...Ch. 4.2 - Prob. 3RCh. 4.2 - Estimate the elevation of point A.Ch. 4.2 - Prob. 2ACh. 4.2 - How far would you walk along the trail from point...Ch. 4.2 - Prob. 4ACh. 4.3 - Prob. 0LOCh. 4.3 - The amount of profit that a company makes when...Ch. 4.3 - If he decides to make the play area 5 feet wide,...Ch. 4.3 - Prob. 2GCh. 4.3 - Prob. 3GCh. 4.3 - Based on the graph, what width makes the area as...Ch. 4.3 - Prob. 5GCh. 4.3 - Prob. 6GCh. 4.3 - Prob. 7GCh. 4.3 - Prob. 8GCh. 4.3 - Prob. 9GCh. 4.3 - Prob. 10GCh. 4.3 - Prob. 11GCh. 4.3 - Prob. 12GCh. 4.3 - Prob. 13GCh. 4.3 - Prob. 14GCh. 4.3 - Prob. 15GCh. 4.3 - Prob. 1TCh. 4.3 - If youre looking at a graph, what are some key...Ch. 4.3 - Prob. 2RCh. 4.3 - Type a short answer to each question. Think of...Ch. 4.3 - Prob. 4RCh. 4.3 - About how high above the ground was the ball when...Ch. 4.3 - How far away from where it was kicked did the ball...Ch. 4.3 - How high did the punt go?Ch. 4.3 - The hang time of a punt is how long its in the air...Ch. 4.3 - After how many seconds was the ball 45 feet above...Ch. 4.3 - Prob. 7ACh. 4.3 - Prob. 8ACh. 4.4 - Prob. 0LOCh. 4.4 - Describe the differences between linear and...Ch. 4.4 - Prob. 2CCh. 4.4 - Prob. 3CCh. 4.4 - Prob. 4CCh. 4.4 - Prob. 5CCh. 4.4 - Prob. 6CCh. 4.4 - Prob. 7CCh. 4.4 - Prob. 8CCh. 4.4 - Prob. 9CCh. 4.4 - Prob. 10CCh. 4.4 - If youre the coffee drinker represented by the...Ch. 4.4 - Find the relative change in caffeine for each...Ch. 4.4 - Complete this important statement about...Ch. 4.4 - Looking at the graph of the caffeine remaining in...Ch. 4.4 - Whats the multiplication factor that youd need to...Ch. 4.4 - Prob. 6GCh. 4.4 - Prob. 7GCh. 4.4 - Prob. 8GCh. 4.4 - Prob. 9GCh. 4.4 - Use either TABLE or TRACE commands on your...Ch. 4.4 - Prob. 11GCh. 4.4 - Compare exponential growth and exponential decay....Ch. 4.4 - What did you learn in this lesson about the value...Ch. 4.4 - Prob. 3RCh. 4.4 - How much money is Joe earning when hes 30?Ch. 4.4 - How much money is he allowing himself to spend...Ch. 4.4 - How much is Joe earning when hes 35? Show a...Ch. 4.4 - How much money is Joe allowing himself to spend...Ch. 4.4 - Carefully explain the meaning of the crossover...Ch. 4.5 - Prob. 0LOCh. 4.5 - Prob. 1GCh. 4.5 - Prob. 2GCh. 4.5 - Prob. 3GCh. 4.5 - Prob. 4GCh. 4.5 - Prob. 5GCh. 4.5 - Prob. 6GCh. 4.5 - Prob. 7GCh. 4.5 - Prob. 8GCh. 4.5 - Prob. 9GCh. 4.5 - Prob. 10GCh. 4.5 - Prob. 11GCh. 4.5 - Prob. 1CCh. 4.5 - Prob. 2CCh. 4.5 - Prob. 3CCh. 4.5 - Prob. 4CCh. 4.5 - Prob. 5CCh. 4.5 - Prob. 6CCh. 4.5 - Prob. 7CCh. 4.5 - Prob. 8CCh. 4.5 - Prob. 9CCh. 4.5 - Prob. 10CCh. 4.5 - Prob. 11CCh. 4.5 - Prob. 12CCh. 4.5 - Prob. 13CCh. 4.5 - Prob. 14CCh. 4.5 - Prob. 15CCh. 4.5 - Prob. 16CCh. 4.5 - Prob. 1RCh. 4.5 - Prob. 2RCh. 4.5 - Prob. 3RCh. 4.5 - Prob. 4RCh. 4.5 - Prob. 1ACh. 4.5 - Prob. 2ACh. 4.5 - Prob. 3ACh. 4.5 - Prob. 4ACh. 4.6 - Prob. 0LOCh. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Prob. 5CCh. 4.6 - Prob. 6CCh. 4.6 - Prob. 7CCh. 4.6 - Prob. 8CCh. 4.6 - Prob. 9CCh. 4.6 - Prob. 10CCh. 4.6 - Prob. 11CCh. 4.6 - Prob. 12CCh. 4.6 - Use Newtons law of universal gravitation to find...Ch. 4.6 - Prob. 14CCh. 4.6 - Prob. 1GCh. 4.6 - Prob. 2GCh. 4.6 - Prob. 3GCh. 4.6 - Prob. 5GCh. 4.6 - Prob. 6GCh. 4.6 - Prob. 7GCh. 4.6 - A fun fact: you can use a microwave oven and a bar...Ch. 4.6 - Prob. 1RCh. 4.6 - Prob. 2RCh. 4.6 - Prob. 3RCh. 4.6 - Prob. 4RCh. 4.6 - Prob. 1ACh. 4.6 - Prob. 2ACh. 4.6 - Prob. 3ACh. 4.6 - Prob. 4ACh. 4.6 - Prob. 5ACh. 4.6 - Prob. 6ACh. 4.6 - Prob. 7ACh. 4.7 - Prob. 0LOCh. 4.7 - Prob. 1GCh. 4.7 - Prob. 2GCh. 4.7 - Prob. 3GCh. 4.7 - Prob. 4GCh. 4.7 - Prob. 5GCh. 4.7 - Prob. 6GCh. 4.7 - Prob. 7GCh. 4.7 - Prob. 8GCh. 4.7 - Prob. 9GCh. 4.7 - Prob. 10GCh. 4.7 - Prob. 11GCh. 4.7 - From years of experience, the owner of a small...Ch. 4.7 - Prob. 13GCh. 4.7 - Prob. 14GCh. 4.7 - Prob. 15GCh. 4.7 - Prob. 16GCh. 4.7 - Prob. 17GCh. 4.7 - Prob. 18GCh. 4.7 - Prob. 19GCh. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - Prob. 5CCh. 4.7 - Prob. 6CCh. 4.7 - Prob. 7CCh. 4.7 - Our next goal is to multiply (x5)by(x2+3x+4). a....Ch. 4.7 - Prob. 9CCh. 4.7 - What is a polynomial? What is meant by the phrase...Ch. 4.7 - Prob. 2RCh. 4.7 - What questions do you have about this lesson?Ch. 4.7 - Prob. 1ACh. 4.7 - Prob. 2ACh. 4.7 - Prob. 3ACh. 4.7 - Prob. 4ACh. 4.7 - Prob. 5ACh. 4.7 - Prob. 6ACh. 4.7 - Prob. 7ACh. 4.7 - Prob. 8ACh. 4.7 - Prob. 9ACh. 4.7 - Prob. 10ACh. 4.8 - Prob. 0LOCh. 4.8 - Perform the multiplication: 57=Ch. 4.8 - Prob. 2GCh. 4.8 - If the volume in the YouTube window is set at half...Ch. 4.8 - If the volume in the YouTube window is set at half...Ch. 4.8 - If the volume in the YouTube window is set all the...Ch. 4.8 - To get the overall volume, we _______ the...Ch. 4.8 - Prob. 7GCh. 4.8 - Prob. 8GCh. 4.8 - Prob. 9GCh. 4.8 - Prob. 10GCh. 4.8 - Prob. 11GCh. 4.8 - Prob. 12GCh. 4.8 - Prob. 1CCh. 4.8 - For the polynomial P(x)=(x1)(x+5), find each...Ch. 4.8 - Use the table and graph provided for...Ch. 4.8 - Prob. 4CCh. 4.8 - Prob. 5CCh. 4.8 - y(x)=(x+5)(x+4)(x2) Zeros: x intercepts:Ch. 4.8 - Prob. 7CCh. 4.8 - Prob. 8CCh. 4.8 - Prob. 9CCh. 4.8 - Prob. 10CCh. 4.8 - Prob. 11CCh. 4.8 - Prob. 12CCh. 4.8 - Prob. 13CCh. 4.8 - Prob. 14CCh. 4.8 - Prob. 15CCh. 4.8 - Prob. 16CCh. 4.8 - Prob. 17CCh. 4.8 - Prob. 18CCh. 4.8 - Prob. 19CCh. 4.8 - If the current yield per tree is 800, and will go...Ch. 4.8 - If the current yield per tree is 800, and will go...Ch. 4.8 - Prob. 22CCh. 4.8 - Prob. 23CCh. 4.8 - Prob. 24CCh. 4.8 - Prob. 1RCh. 4.8 - Prob. 2RCh. 4.8 - Prob. 3RCh. 4.8 - Prob. 1ACh. 4.8 - Prob. 2ACh. 4.8 - Prob. 3ACh. 4.8 - Prob. 4ACh. 4.8 - Prob. 5ACh. 4.8 - Prob. 6ACh. 4.9 - Prob. 0LOCh. 4.9 - Prob. 1CCh. 4.9 - Use the quadratic formula to find the two...Ch. 4.9 - One of the solutions provides the length of the...Ch. 4.9 - What is the significance of the other solution in...Ch. 4.9 - Whats the connection between the solutions of the...Ch. 4.9 - Prob. 6CCh. 4.9 - Prob. 7CCh. 4.9 - Prob. 8CCh. 4.9 - Prob. 9CCh. 4.9 - Prob. 10CCh. 4.9 - Prob. 1GCh. 4.9 - Prob. 2GCh. 4.9 - Prob. 3GCh. 4.9 - Prob. 4GCh. 4.9 - Prob. 5GCh. 4.9 - Prob. 6GCh. 4.9 - Experiment: The Time Needed To Drain a Bottle...Ch. 4.9 - Prob. 8GCh. 4.9 - Experiment: The Time Needed To Drain a Bottle...Ch. 4.9 - What is the quadratic formula used for? Why is...Ch. 4.9 - What types of applied problems can be solved using...Ch. 4.9 - Prob. 3RCh. 4.9 - Use a calculator or spreadsheet to make a table of...Ch. 4.9 - Find the vertex of the parabola using the formula...Ch. 4.9 - Explain what each coordinate of the vertex means.Ch. 4.9 - Find the intercepts for the function.Ch. 4.9 - Explain what each intercept means.Ch. 4.9 - Describe when the ball is headed upward, and when...Ch. 4.9 - Prob. 7ACh. 4.9 - The distance for golf shots is traditionally...Ch. 4.9 - Prob. 9ACh. 4.9 - Prob. 10ACh. 4.9 - Prob. 11ACh. 4.9 - Prob. 12ACh. 4.10 - After reading the opening paragraph, what do you...Ch. 4.10 - Record the data from your experiment in the table....Ch. 4.10 - Use these data to create a scatter plot. Use the...Ch. 4.10 - Using your graphing calculator, find an...Ch. 4.10 - Use your function to approximate the height of the...Ch. 4.10 - Evaluate your equation for x=0. What does your...Ch. 4.10 - What does the variable x represent?Ch. 4.10 - In the equation y=abx that models your data, what...Ch. 4.10 - In the equation y=abx that models your data, what...Ch. 4.10 - Using data from your original table, fill in this...Ch. 4.10 - Use these data to create a second scatter plot.Ch. 4.10 - Based on the scatter plot, what kind of equation...Ch. 4.10 - Use your graphing calculator to find the equation...Ch. 4.10 - Your equation has a variable in it, but also has...Ch. 4.10 - If you were to drop the golf ball from your...Ch. 4.10 - Find the relative change in height from one bounce...Ch. 4.10 - (This one requires some thought, but is the key...Ch. 4.10 - Whats the bounce height as a percentage of the...Ch. 4.10 - Write an expression that calculates the bounce...Ch. 4.10 - Write an equation that describes the bounce height...Ch. 4.10 - Using your answer to Question 17, its possible to...Ch. 4.10 - What do you think would be some sources of error...Ch. 4.10 - Type a short answer to each question. Weve studied...Ch. 4.10 - How could you tell if neither of those types of...Ch. 4.10 - Type a short answer to each question. Take another...Ch. 4.10 - What questions do you have about this lesson?Ch. 4.10 - The equation y=10,000(1.06)x describes the growth...Ch. 4.10 - Prob. 2ACh. 4.10 - The equation y=10,000(1.06)x...Ch. 4.10 - The model in Questions 1-3 is an example of...Ch. 4.10 - The model in Questions 1-3 is an example of...Ch. 4.10 - When an initial amount of P dollars is invested at...Ch. 4.10 - Prob. 7ACh. 4.10 - When an initial amount of P dollars is invested at...Ch. 4.10 - When an initial amount of P dollars is invested at...Ch. 4.10 - One of the best reasons for understanding...Ch. 4.10 - One of the best reasons for understanding...Ch. 4.10 - One of the best reasons for understanding...Ch. 4.10 - One of the best reasons for understanding...
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- 5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forward
- Problem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forwardWhat is the standard scores associated to the left of z is 0.1446arrow_forward2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forward
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- 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forwardThe general solution X'=Ax is given. Discuss the nature of the solutions in a neighborhood of (0,0) -2-2 (²) |a) A = (23) X(A) = (₁ (fi)e* + (2 (2) eht -2-5arrow_forward
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